The universe has a non-zero temperature from its beginnings until today. Then the temperature is an important ingredient in nature and must be considered when studying any phenomenon. These thermal effects are present in all known phenomena of the standard model and general relativity. There are two approaches to introducing temperature into a theory. One of them is the imaginary-time formalism which consists of replacing \(\displaystyle t\) , with a complex time, \(\displaystyle i\tau \)  [1]}. Then the temporal information of the system is lost. The other is the real-time formalism. In this case, there are two distinct, but equivalent approaches. (i) Closed time path formalism [2]}, where the degrees of freedom of the system are doubled and the Green's function assumes a matrix structure. (ii) Thermo Field Dynamics (TFD) formalism [3]}, [4]}, [5]}, [6]}, [7]}, [8]}. This procedure is built from the ideas that consider the statistical average of an operator equal to the vacuum expectation value of this operator. For such an interpretation to be possible, two elements are necessary: the Hilbert space must be duplicated and the Bogoliubov transformation is used. Another characteristic of this formalism is its topological structure that allows studying different phenomena on an equal footing, such as the Stefan-Boltzmann law and the Casimir effect. In this paper, the TFD formalism is used and three different topologies are investigated.
